13/07/2023, 12:00 — 12:30 — Online
António Lages, Instituto Superior Técnico, Universidade de Lisboa
Nested Quandles
In this talk we elaborate on our last doings: the definition of a new family of quandles and the production of infinitely many examples of such quandles. These quandles are defined for having a profile made up of lengths pairwise distinct (which makes them connected quandles, thanks to our previous work) and also that each length divides the larger lengths. We prove that if we fix the number of lengths to be $c$, then the profile of these quandles is made up of $c$ lengths, the first two being $1$ and $l$ (where $l+1$ equals a prime power) and then $l_i = l(l+1)^{i-2}$. We call them Nested Quandles because they have subquandles with similar profiles. Time permits we elaborate on the examples of these quandles that we constructed.
